Universal time delay in static spherically symmetric spacetimes for null and timelike signals *

Abstract

Abstract A perturbative method of computing the total travel time of both null and lightlike rays in arbitrary static spherically symmetric spacetimes in the weak field limit is proposed. The resultant total time takes a quasi-series form of the impact parameter. The coefficient of this series at a certain order n is shown to be determined by the asymptotic expansion of the metric functions to the order . For the leading order(s), the time delay, as well as the difference between the time delays of two types of relativistic signals, is shown to take a universal form for all SSS spacetimes. This universal form depends on the mass M and a post-Newtonian parameter of the spacetime. The analytical result is numerically verified using the central black hole of galaxy M87 as the gravitational lensing center.